Find the greatest common factor of $90$ and $135$.
Explanation: The greatest common factor (GCF) is the largest number that is a factor of both $90$ and $135$. In order to find the GCF, we can factor each number completely as a product of prime numbers: $ \begin{aligned}90 &=2\cdot3\cdot3\cdot5\\\\\\\\ 135&=3\cdot3\cdot3\cdot5 \end{aligned}$ Now, let's find the factors that are common to each number: $ \begin{aligned}90 &=2\cdot3\cdot3\cdot5\\\\\\\\ 135&=3\cdot3\cdot3\cdot5 \end{aligned}$ Each number shares the factors ${3}, {3},$ and $5,$ so the GCF is $3\cdot3\cdot5={45}$. The greatest common factor of $90$ and $135$ is $45$.